Scientific Research of the Institute of Mathematics and Computer Science ON PLANE CONTACT PROBLEM OF AN ELASTIC PERIODICALLY LAYERED COMPOSITE WITH BOUNDARY NORMAL TO LAYERING Dariusz M. Perkowski Faculty of Mechanical Engineering, Bialystok University of Technology, Bialystok, Poland email: dmperkowski@doktoranci.pb.edu.pl Abstract. This paper deals with some plane contact problem of an elastic laminated half- plane with boundary normal to layering. The considered problem is solved within the framework of the homogenized model with microlocal parameters given by Woźniak [6], Matysiak and Woźniak [7]. The body is assumed to be composed of two-layered, perio- dically repeated laminae. The perfect mechanical bonding between the layers is assumed. Moreover, the boundary condition for normal stresses on boundary normal to layering is approximated by using approach given by Perkowski et al. [8], Matysiak and Perkowski [9]. This approach allows to reduce the described problem to well-known dual integral equa- tions and it can be solved exactly. Thus, the problem is solved by using analytical methods. The results of numerical analyses shown the distribution of contact pressure and stress distributions are presented in the form of figures. Introduction The construction elements, which are working in contact with another elements can be endangered to high contact pressures. The modelling of contact problem is very important from the engineering point of view and it was developed by many researchers, for example [1-5]. The contacted bodies considered in these mono- graphs were homogenous. For the periodically layered composites, the contact problems with the boundary parallel to the layering were developed in [6-8]. In this paper, the periodically layered elastic half-plane with the boundary perpen- dicular to the layering is considered. Such medium is described within the frame- work of theory of elasticity by partial differential equations with discontinuous, oscillating coefficients. The application of this approach to solve the considered problem is rather complicated. So, the natural way is applied some approximated method, which allows to simplify the formulated problem. Some of them is homogenized model with microlocal parameters given by Woźniak [9-11] and applied to layered composites by Matysiak and Woźniak [12]. This approach was derived by using the concepts of nonstandard analysis combined with some postu- lated a priori physical assumptions. The equations of the homogenized model are Please cite this article as: Dariusz M. Perkowski, On plane contact problem of an elastic periodically layered composite with boundary normal to layering, Scientific Research of the Institute of Mathematics and Computer Science, 2007, Volume 6, Issue 1, pages 205-218. The website: http://www.amcm.pcz.pl/